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A Dynamic Penalty or Projection Method for Incompressible Fluids

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Abstract

In a previous work (Angot et al. in J. Comput. Appl. Math. 226:228–245, 2009), some penalty–projection methods have been tested for the numerical analysis of the Navier-Stokes equations. The purpose of this study is to introduce a variant of the penalty–projection method which allows us to compute the solutions faster than by using the previous solver. This new variant combines dynamically and alternatively a penalty procedure and a projection procedure according to the size of the divergence of the velocity. In other words, this study aims to prove that it is possible to project the intermediate velocity, computed by the first step of the penalty–projection method, only if its divergence is larger than a specified threshold. Theoretical estimates for the new method are given, which are in accordance with the numerical results provided.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Informatique et Applications, Université des Antilles et de la Guyane, Campus de Fouillole BP 250, Pointe-à-Pitre, 97157, Guadeloupe F.W.I., France

    J. Laminie & P. Poullet

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  1. J. Laminie
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  2. P. Poullet
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Correspondence to P. Poullet.

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The authors are pleased to acknowledge the “Centre Commun de Calcul Intensif de l’Université des Antilles et de la Guyane” where the comptutational tests have been performed (see http://www.univ-ag.fr/c3i).

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Laminie, J., Poullet, P. A Dynamic Penalty or Projection Method for Incompressible Fluids. J Sci Comput 50, 213–234 (2012). https://doi.org/10.1007/s10915-011-9480-8

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  • DOI: https://doi.org/10.1007/s10915-011-9480-8

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